Is there a Distress Risk Puzzle in the Norwegian Market?
A hazard model approach
Jonas Himberg Sørlie & Snorre Lindseth Nitter
Supervisor: Jørgen Haug
Master thesis, Financial Economics
NORWEGIAN SCHOOL OF ECONOMICS
This thesis was written as a part of the Master of Science in Economics and Business Administration at NHH. Please note that neither the institution nor the examiners are responsible − through the approval of this thesis − for the theories and methods used, or results and conclusions drawn in this work.
Bergen, Fall 2018
Preface
This thesis was written as part of our Master of Science in Economics and Business Administration at the Norwegian School of Economics (NHH). Our specialization is within Financial Economics, and this thesis is a dive into one of the most fundamental themes in the financial literature; the relationship between risk and return.
It has been rewarding to work on this thesis, and we feel fortunate for the opportunity to indulge ourselves in such an interesting topic.
We would like to thank our supervisor, Jørgen Haug, for valuable guidance, insight and inspiration.
Oslo, December 2018
A fundamental principle in the financial literature is that assets with exposure to systematic risk should be compensated with a risk premium in returns. Thus, assuming financial distress risk is systematic, rational investors are expected to demand a premium for holding stocks with exposure to financial distress. However, several academic papers find anomalously low returns for stocks with a high degree of financial distress. This anomaly is referred to as the
“distress risk puzzle”.
In this paper we explore the relationship between distress risk and stock returns for publicly traded companies in Norway in the period from June 2004 to September 2018. We use default probability as a proxy for financial distress and estimate default probabilities by incorporating Campbell, Hilscher and Szilagyi’s (2008) best model. We allocate the stocks into eight different portfolios depending on their level of financial distress and measure the respective returns of the different portfolios. The returns are measured for three months, before the portfolios are re-balanced based on updated default probabilities.
Assuming distress risk is systematic, we would expect the distressed stocks to carry a premium. Thus, our null hypothesis is that investors who hold the most distressed stocks in the market over time will receive a risk premium. However, we find that the portfolio with the most distressed stocks significantly underperforms the portfolio with the least distressed stocks. This finding is also prevalent in risk-adjusted returns, estimated by regressing the portfolio returns on the risk factors in the Fama-French three-factor model. We also find that the most distressed firms on average are smaller in size, have higher market-to-book ratios and a higher degree of leverage.
From the results of our analysis, we can reject the null hypothesis that the most distressed stocks carry a premium. This indicates that there is a distress risk puzzle in the Norwegian market.
1. INTRODUCTION ... 1
2. THEORY ... 4
3. LITTERATURE REVIEW ... 7
4. DISTRESS RISK MODEL ... 10
4.1 HOW TO MEASURE DISTRESS RISK? ... 10
4.2 LITERATURE REVIEW-ECONOMETRIC DEFAULT PROBABILITY MODELS ... 13
4.3 MODEL EXPLANATION ... 15
4.4 MODEL EVALUATION ... 20
5. DATA ... 23
5.1 DATA COLLECTION &PROCESSING ... 23
5.2 SUMMARY STATISTICS ... 27
6. RESULTS ... 31
6.1 PORTFOLIO FORMATION AND RETURN CALCULATION ... 31
6.2 RETURNS OF THE DISTRESS RISK SORTED PORTFOLIOS ... 33
6.3 PORTFOLIO CHARACTERISTICS AND FAMA FRENCH REGRESSION LOADINGS... 37
7. CRITICISM OF THESIS ... 44
7.1 LENGTH OF RETURN MEASURES ... 44
7.2 EXPECTED RETURNS VS.REALIZED RETURNS ... 45
7.3 SINGLE SORTS VS.DOUBLE SORTS ... 45
8. CONCLUSION ... 47
9. REFERENCES ... 49
1. Introduction
A fundamental principle in asset pricing theory is that investors should be compensated for bearing systematic risk. That is, investors should be compensated for holding assets with exposure to risk factors that cannot be diversified away. In asset pricing literature, financial distress has been highlighted as one such systematic risk factor (Chan & Chen, 1991; Fama &
French, 1993; 1995). However, several academic papers find contradictory results; they find that financially distressed stocks earn anomalously low returns (Dichev, 1998; Griffin &
Lemmon, 2002; Garlappi, Shu, & Yan, 2008; Campbell, Hilscher, & Szilagyi, 2008). This anomaly is referred to as the “distress risk puzzle”.
The majority of these papers examine the relationship between distress risk and stock returns in the American market, and to the best of our knowledge, no paper conducts a thorough examination on the Norwegian market1. Thus, we have found it valuable to research the phenomenon in Norway. As we expect distressed stocks to carry a premium, our null hypothesis is that investors who hold the most distressed stocks in the market over time will receive a risk premium. A potential rejection of the null hypothesis is indicative of a distress risk puzzle in the Norwegian market. In our paper, we use default probability as a proxy for distress risk. That is, a company that is predicted to have a high default probability is assumed to have a high level of financial distress. We allocate stocks into eight different portfolios depending on their level of financial distress, and measure the respective returns of the different portfolios. The returns are measured from the beginning of June 2004 to the beginning of September 2018, and the portfolios are re-balanced every third month based on updated default probabilities.
We find that the portfolio with the most distressed stocks significantly underperforms relative to the portfolio with the least distressed stocks. Moreover, our results indicate that stock performance is negatively correlated with distress risk. We also find that the most distressed firms on average are smaller in size, have higher market-to-book ratios and a higher degree of leverage.
1 Eisdorfer, Goyal and Zhdanov (2018) conducts a global study of which Norway is included, however there is no in-debt analysis of the Norwegian results. We will discuss this in more detail in Chapter 3.
The starting point for the thesis is a discussion regarding the relationship between risk and return in general, building a theoretical framework for understanding risk factors as a source of return premium. In light of this theoretical framework, we discuss the association between distress risk and realized returns. Furthermore, we discuss bankruptcy risk as a proxy for distress risk.
In Chapter 3, we review existing research that is conducted on the relationship between financial distress and stock returns.
Next, in Chapter 4, we start with describing common proxies for distress risk and elaborate on why we found an econometric model for default prediction to be the best proxy for distress risk in Norway. Next, we conduct a literature review on econometric models to further elaborate on why we chose our specific model. After that, we go through our preferred model in more detail, before we end the chapter with discussing the predictive power of the model on Norwegian data.
After that, in Chapter 5, we describe our dataset. We discuss how we collected and processed the data in order to use it as input in the default probability model. In addition, we showcase statistical properties of the final dataset.
In Chapter 6, we analyze the relationship between distress risk and stock returns in the Norwegian market. We begin by describing how the portfolios are formed and re-balanced as well as how we measure the portfolios performance. Next, we perform paired t-tests to compare the returns between the most distressed portfolios against the least distressed portfolios. Subsequently, we turn our attention towards the characteristics of the different distress risk sorted portfolios. In order to strengthen this analysis, we also regress the quarterly returns on the factors in the Fama-French three-factor model. This is to better examine the portfolios characteristics, as well to assess the risk-adjusted returns. The results reveal that the portfolio with the most distressed stocks have high loadings on all the risk factors, and that this portfolio underperforms the other portfolios with a significant negative unexplained return.
Next, in Chapter 7, we discuss potential short-comings of the thesis. This includes a discussion of the time-frame of which we measure returns for the sorted portfolios before they are re- balanced. Furthermore, we discuss realized returns as a proxy for expected returns. We end
this chapter with a discussion regarding the implications of single-sorting on distress risk versus double-sorting on characteristics and distress risk.
Finally, we summarize our findings in a conclusion and utilize the opportunity to elaborate on potential extensions to the thesis.
2. Theory
The first asset pricing model that explained an equity´s expected return based on its exposure to systematic factor risk was the Capital Asset Pricing Model, also known as CAPM (Ang, 2014). In CAPM, there is only one risk factor; the market portfolio. According to CAPM, the expected excess return of a stock is solely decided by the stock´s exposure to the market factor (Ang, 2014). A higher exposure to the market factor should be compensated with higher expected returns.
Since the introduction of CAPM, several studies argue that the model fails to reflect reality (Ang, 2014). However, the model is still valuable as it provides insight into how a stock´s risk premium is determined by its exposure to underlying risk factors. Since CAPM, several multifactor models have been developed to explain the return of a stock based on risk factors.
The most used multifactor models today are variations of the Fama-French three-factor model, which was introduced by Fama and French in 1993. In the three-factor model, a stock´s excess return is explained by its exposure to three factors; the market factor from CAPM, a SMB factor and a HML factor (Fama & French, 1993). The SMB factor is a constructed portfolio that buys stocks with a small market capitalization and sells stocks with a large market capitalization. SMB is adjusted for the variation in book-to-market equity. Thus, the goal is to mimic the cross-sectional variation in returns associated with size (Fama & French, 1993). On the other hand, HML is a portfolio where the goal is to mimic the cross-sectional variation in returns associated with variations in book-to-market equity, corrected for the variation in size (Fama & French, 1993). The HML portfolio buys stocks with a high book-to-market equity ratio and sells stocks with a low book-to-market equity ratio. In other words, the HML portfolio goes long in value stocks and short in growth stocks.
In more recent years, the three-factor model has been extended, and today there exist several different versions that include other factors such as momentum, operating profitability and investment patterns (Carhart, 1997; Fama & French, 2015). We will not discuss these factors in further detail. Instead, we will elaborate on how distress risk, which is the topic of this thesis, can be linked to priced risk factors.
Distress risk is believed to be one of the underlying drivers that can explain the positive returns associated with SMB and HML (Chan & Chen, 1991; Fama & French, 1992). A firm in
financial distress will have trouble paying off its creditors, and the state of financial distress can lead to several costs. The costs often associated with financial distress are increased cost of capital, having to sell off assets at low prices, decreased customer loyalty and having to desist from attractive investment opportunities (Altman, 1984; Andrade & Kaplan, 1998;
George & Hwang, 2010). It is reasonable to argue that companies are more likely to incur such costs when the economy is in a low state, and that the cost of distress thus increases the exposure to systematic risk (George & Hwang, 2010). Accordingly, several papers find evidence that the premium observed in the Fama-French risk factors can be explained by exposure to distress risk.
Chan and Chen (1991) argue that small firms carry a value premium over large firms because they tend to have a higher degree of financial distress. They argue that these firms are marginal firms which are more sensitive to changes in the economy and less likely to survive periods of low economic growth (Chan & Chen, 1991). Furthermore, Fama and French (1992; 1995) find evidence of financial distress as a potential explanation of the book-to-market effect2 captured by the HML factor. They argue that firms with high book-to-market ratios have higher distress risk than their low book-to-market counterparts, and that they experience a risk premium in returns (Fama & French, 1992; 1995). Furthermore, Ferguson and Shockley (2003) argue that relative leverage and relative distress can explain the return premiums associated with exposure to the SMB factor and the HML factor.
These studies indicate that distress risk is a priced systematic factor. However, if distress risk is systematic, stocks with high distress risk should receive a premium in returns relative to stocks with low distress risk. Nevertheless, several academic papers find contradictory results, which is the anomaly referred to as the distress risk puzzle.
We use default probability as a proxy for distress risk and assume that a company’s bankruptcy risk is closely related to its distress risk. However, it should be noted that there are conflicting evidence in the financial literature regarding the relationship between default probability and distress risk. George and Hwang (2010) argue that a firm´s probability of default does not necessarily reflect its exposure to distress risk. They argue that firms with high exposure to
2 The book-to-market effect is the phenomenon that firms with high book-to-market ratios tend to outperform firms with low book-to-market ratios (Ang, 2014).
distress risk choose lower leverage, and thus reduce their probability of default. Nevertheless, it is also reasonable to argue that default probability is closely related to distress risk as a company that has a high probability of default is likely to incur costs related to financial distress. Thus, in this paper, we assume that default probability is a good proxy for distress risk. In the next chapter, we will further elaborate on existing research on the relationship between distress risk and return.
3. Litterature Review
Several papers have investigated the relationship between financial distress and stock returns, but their methods and findings vary.
Dichev (1998) examines the returns of U.S. industrial firms in the period from 1981 to 1995.
He uses bankruptcy risk as a proxy for distress risk and estimates bankruptcy risk by using both Altman´s Z-score (1968) and Ohlson´s O-score (1980). The Z-score was developed using a multiple discriminant statistical methodology, while the O-score was developed using a conditional logit specification, and they were both estimated based on financial ratios (Altman, 1968; Ohlson, 1980). These scores are further elaborated in Chapter 4.2. Dichev runs regressions with returns as the dependent variable and bankruptcy risk, market capitalization and book-to-market ratio as independent variables. He finds that the returns of industrial companies decrease with increasing distress risk. That is, his research suggest that financially distressed firms underperform relative to less distressed firms, even when adjusting for the size and book-to-market effects.
Griffin and Lemmon (2002) also uses the Ohlson´s O-score as a proxy for financial distress when they examine U.S. stock returns in the period from July 1965 to June 1996. They find evidence against distress risk as a source of return premium. They group the companies in the dataset based on their book-to-market values and find that for the high book-to-market group, the distressed stocks have approximately similar returns as the stocks with low distress risk.
One the other hand, for the low book-to-market group, the distressed stocks receive exceedingly low returns compared to the stocks with low distress risk. Consequently, Griffin and Lemmon argue that Dichev’s results largely can be ascribed to the weak performance of low book-to-market stocks.
Vassalou and Xing (2004) uses Merton’s (1974) option pricing model3 to estimate companies likelihood of default, and they use this measure as a proxy for distress risk. They examine the relationship between default risk and equity returns in the U.S. in the period from 1971 to 1999. They find that financially distressed firms outperform firms with less financial distress only to the extent that they have a high book-to-market ratio and small market capitalization
3 Further elaborated in Section 4.1
(Vassalou & Xing, 2004). Furthermore, they point out that the book-to-market effect and the size effect is closely linked to distress risk, as they only find these effects for stocks with high distress risk.
Garlappi et al. (2008) examines the relationship between default risk and stock returns for non- financial U.S. firms in the period from 1969 to 2003. They utilise the Expected Default Frequency measure from Moody´s KMV4 to estimate the default probability and use this as a proxy for distress risk. This measure of distress risk is very similar to the one used in Vassalou and Xing (2004), as it is based on Merton’s option pricing model. They find that default probability and returns, in general, are not positively related (Garlappi et al., 2008)
Campbell et al. (2008) continue the line of research on the return of financially distressed stocks. As will be described in detail later, they develop a logit model to calculate ex-ante default probabilities. They use these default probabilities to allocate stocks into different portfolios and examine the returns for U.S. companies in the period from 1981 to 2003. They find that financially distressed stocks tend to deliver anomalously low returns (Campbell et al., 2008).
George and Hwang (2010) investigate the relationship between financial distress, leverage and returns in the U.S. As part of their study, they use Ohlson´s O-score as a proxy for financial distress and examine the relationship between distress risk and returns from 1966 to 2002.
They find that firms with high distress risk earn low returns relative to firms with low distress risk. Furthermore, they find that the distress risk puzzle is more prevalent when the returns are risk adjusted. However, they argue that default probability is a poor measure for capturing systematic distress risk.
Chava and Purnanandam (2010) examine the relationship between stock returns and default risk for U.S. firms in the period from 1953 to 2006. They estimate a hazard model for default probability following Shumway (2001) and others, in addition to a distance to default measure based on Merton’s (1974) option pricing model. Both these models are used as proxies for distress risk. In contrast to previous studies, they use the analysts expected returns instead of realized returns, arguing that this better captures the real relationship between financial distress
4 Moody’s KMV is a credit risk product developed to estimate default, and the algorithm is based on Merton’s option pricing model (Moody's KMV).
and stock returns. In addition, they measure returns for a longer time horizon than previous studies. They find a strong positive correlation between financial distress and expected stock returns for the larger part of their sample period. However, for the period between 1980 and 1990, they find a negative relationship between financial distress and expected stock returns.
Eisdorfer et al. (2018) study the performance of financially distressed companies in the period from 1992 to 2010. They have a global approach, and study companies from 34 different countries using Merton´s distance-to-default model as an estimate of default risk. They find that the distress anomaly is a phenomenon that is prevalent only in developed countries, and not in emerging markets (Eisdorfer et al., 2018). In their study, they report the performance of a long – short portfolio in the Norwegian market that buys the 20% most distressed stocks and sells the 20% least distressed stocks. This portfolio achieves a negative monthly excess return of – 0.43%. The T-statistic is low at -0.83. This is a mild indication of the existence of a distress risk puzzle in the Norwegian market. However, as they conduct a global study, no in- depth analysis is conducted for Norway. We therefore view our research on the Norwegian market as a relevant in depth-study to further examine the existence of a distress risk puzzle in Norway.
As shown in existing literature, there are mixed findings regarding the relationship between distress risk and stock returns, and a range of different measures have been used as proxies for distress risk. There have also been several attempts at explaining the anomaly in returns of distressed stocks, but as yet no consensus has been reached.
4. Distress Risk Model
In this chapter, we will first discuss common proxies for distress risk and explain why we chose an econometric model for default probability as our proxy for distress risk on Norwegian firms. Secondly, we will take the reader through a literature review on the development in econometrically based default probability models, to elaborate on our choice of model. In the third section, we will explain our preferred model, while the last section is a discussion on the predictive power of the model on Norwegian data.
4.1 How to Measure Distress Risk?
In order to do an analysis on the distress risk puzzle, an accurate measure of distress risk is needed. A company’s credit rating, the yield on bonds and the probability of default are all proxies that can be used to indicate a company’s level of financial distress.
We will start by discussing credit rating as a proxy for distress risk. The U.S. Securities and Exchange Commission (2017) defines credit rating as an assessment of an entity’s creditworthiness, that is, an entity’s ability to cover its financial obligations. It is the credit rating agencies that perform the credit ratings based on their own analytical models, assumptions and expectations (U.S. Securities and Exchange Comission, 2017). The results typically range from the best rating AAA, to the lowest rating D, of which the latter represents default. Thus, credit rating is closely linked to credit risk; low credit rating implies high credit risk, and hence, high probability of default. Therefore, credit rating can be used as a proxy for distress risk. That is, we can assume that the distress risk increases as credit rating decreases.
However, because of strict regulations in the Norwegian market, the credit rating agencies were unable to supply us with credit ratings on Norwegian firms. In addition, knowing that the agencies use their own analytical models, assumptions and expectations in forming the credit ratings, it is uncertain how extensive the research behind each rating actually is.
Furthermore, a credit rating approach implicitly relies on the assumption that all assets within one rating share the same distress risk. In other words, there are several aspects that makes a credit rating approach unsuitable in the Norwegian market.
Next, we would like to discuss the yield of corporate bonds as a proxy for distress risk. The yield of a bond essentially depends on three factors; the risk-free rate, the specifications5 in the bond contract and the company’s default probability (Merton, 1974). Thus, the differences in yield between two corporate bonds with the same specifications will reflect the difference in default probability between the two underlying companies. More generally; the higher the default risk, the higher the spread between the risk-free rate and the bond yield, everything else equal. That is, it would be possible to get a proxy for distress risk by looking at the relative yield spread of the bonds in the market.
In order to do so, a sufficient quantity of liquid corporate bonds must be available to analyze in the market. This immediately limits our potential dataset to companies with corporate bonds that are frequently traded. Only a minority of the companies listed in Norway have corporate bonds that fulfils this requirement. In addition, when taking into consideration that the bonds must be similar in the specifications in order to compare the relative yields, the potential dataset is likely to be insufficient to draw conclusions. In addition, Elton, Gruber, Agrawal and Mann (2001) provide evidence that the spreads of corporate bonds are closely linked to the risk factors accepted for common stocks, and that only a small portion is related to default probability. This suggests that we should adjust for size and book-to-market values for the underlying companies in addition to adjusting for the bond specifications, which will further diminish the possible comparable bonds. With this in mind, we have concluded that using yield spreads as a proxy for distress risk is unfavorable for researching the distress risk puzzle in Norway.
Finally, we will discuss models that are developed to indicate companies likelihood of default.
There are two different approaches that we will discuss; the option pricing approach and the econometric approach. The option pricing approach is typically based on the structural default model of Merton (1974), and the idea that a firm’s equity can be considered a call option on the underlying value of the firm, with strike price equal to the face value of the debt. The option pricing approach has several advantages. Firstly, this approach depends on a limited set of variables which are easily available. Furthermore, the model incorporates equity values which contain forward-looking information, as equity values reflect the investors future perspectives. It is reasonable to assume that using forward-looking measures is better when
5 Maturity date, seniority in case of default and security in assets etc.
predicting the likelihood of default in the future. However, an option pricing approach relies on several assumptions that are likely not to hold in the real world. It relies on the assumption of a frictionless market, that all firms have issued just one zero-coupon bond and that the underlying value of the firms follow a geometric Brownian motion (Bharath & Shumway, 2008).
The econometric approach, on the other hand, typically uses a logit specification where a bankruptcy indicator6 is regressed on several accounting and market variables in order to estimate a model for default probability. The advantage of these models is that it does not rely on the assumptions that are present in the option pricing models. In addition, accounting and market data are publicly available for all Norwegian firms listed on Oslo Børs, Oslo Axess and Merkur Markets. Furthermore, as we will elaborate in the next section, econometric models have improved over recent years and have proven to be accurate predictors for default probability (Campbell et al., 2008). Earlier, econometric models were criticized for being backward-looking as they only included variables found in the accounting data published in the quarterly reports (Vassalou & Xing, 2004). The new models, however, have incorporated market data, which means that stock market developments and volatility measures are included as predictors for default probability. Hence, one can argue that the models have developed to incorporate a forward-looking aspect.
In the process of evaluating whether the option pricing approach or the econometric approach is best suited as a proxy for distress risk on Norwegian data, we have emphasized the findings of Campbell et al. (2008) and Bharath and Shumway (2008). Campbell et al. (2008) finds that a distance to default measure based on an option pricing approach adds little explanatory power when included in their best econometric model. Furthermore, they find that the pseudo- R2 of a pure option pricing model is only half as big as the pseudo-R2 for their best econometric model when predicting default. Bharath and Shumway (2008) find similar results when they examine the accuracy of Merton’s distance to default model against an econometric model.
However, they find that econometric logit models perform slightly better when incorporating the Merton’s distance to default measure together with other covariates in out-of-sample predictions (Bharath & Shumway, 2008). In addition to the findings from these papers, we
6 1 if Bankrupt, 0 otherwise
have emphasized the fact that an option pricing approach is based on underlying assumptions that do not hold in the real world.
Thus, after evaluating different opportunities for distress risk proxies on Norwegian data, we have found that an econometric approach, based on an integrated set of accounting and market data, is best suited. However, since there are relatively few listed companies in Norway, the number of bankruptcies are also very limited. Thus, we have chosen to use a model that is developed in the U.S. instead of estimating a model on a limited set of Norwegian data. In order to elaborate on our choice of model, we have conducted a literature review on the development in econometric default probability models in the subsequent section.
4.2 Literature review- Econometric Default Probability Models
The literature review will start with Altman`s Z-score in 1968 and end with Campbell, Hilscher and Szilagyi`s dynamic hazard model in 2008. The latter is our model of choice for predicting distress risk on Norwegian listed companies.
Several studies have been conducted in order to estimate an econometric default probability model. Altman (1968) used a multiple discriminant analysis to study the likelihood of default of publicly traded manufacturing companies. By using financial ratios collected from the companies annual reports, he gave each company a Z-score which could be used to predict bankruptcy within two years (Altman, 1968). Later, Ohlson (1980) developed a logit model for bankruptcy prediction where he extended the research to include a more comprehensive set of companies and found that a wider selection of accounting data significantly improved the predictive power of the default probability model. Shumway (2001) took it further and developed a hazard model to allow for time varying covariates and included both accounting data and market data in the model. Shumway argues that Altman’s and Ohlson’s models are inappropriate in forecasting bankruptcy because they are what he refers to as static models, which are unable to capture the fact that firm characteristics change from year to year (Shumway, 2001).
In the article “Bankruptcy Prediction with Industry Effects” Chava and Jarrow (2004) validate the superiority of Shumway’s dynamic hazard model over previous static models. In addition, Chava and Jarrow improve the research from Shumway by including monthly market data and
quarterly accounting data in their model, which they find to significantly improve the forecasting ability (Chava & Jarrow, 2004). Furthermore, they find that industry effects are statistically significant and that the inclusion of industry effects improves the model’s ability to predict default.
Campbell et al. (2008) chose to construct a new empirical measure of financial distress, building on the work from Shumway (2001), Chava and Jarrow (2004) and others. Based on monthly U.S. bankruptcy data from January 1963 to December 1998 and failure data7 from January 1963 to December 2003, they estimate a hazard logit model of bankruptcy and failure (Campbell et al., 2008). The main difference from Chava and Jarrow’s model is that Campbell, Hilscher and Szilagyi found three more variables with explanatory power; market-to-book ratio, share price and corporate cash holdings. In addition, they found that market value of equity had stronger explanatory power than book-value of equity for variables that included total assets. Furthermore, Campbell et al. (2008) added lagged information about profitability and stock returns to capture the fact that a long history of losses or stock decline is a better indicator of default probability than a sudden drop in income or stock prices. Lastly, Campbell et al. (2008) test for industry effects, but they find that the inclusion of these effects does not add explanatory power in their best model.
Campbell, Hilscher and Szilagyi’s best model incorporate both market data and quarterly accounting variables, and they show that their best model is better than an option pricing approach in predicting default probability. Thus, we have chosen to use their best model on Norwegian data. The next section will explain the model in more detail.
7 Failure data= Companies with financially driven delisting’s and/or companies that receives a D (default) from credit rating agencies
4.3 Model Explanation
Campbell et al. (2008) develop a hazard model that uses logistic regression to estimate probability of default for U.S. listed firms. We use their best model for predicting default one month ahead, which they present in the last column in Table III (Campbell et al., 2008, p.
2910). With inspiration from Li, Lockwood and Miao (2017) we have slightly changed the mathematical notation of Campbell, Hilscher and Szilagyi’s model to make it more intuitive.
We calculate the default probability (DP) for company i in month t by calculating the probability that the company will fail to meet its financial obligations (Y=1) in the following month8, as follows:
𝐷𝑃𝑖,𝑡 = 𝑃𝑖,𝑡(𝑌𝑖,𝑡+1 = 1) = 1 1 + 𝑒(−𝑧𝑖,𝑡)
Where:
𝑧𝑖,𝑡 = −9.08 − 29.67 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑖,𝑡 + 3.36 𝑇𝐿𝑀𝑇𝐴𝑖,𝑡− 7.35 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑖,𝑡+
1.48 𝑆𝐼𝐺𝑀𝐴𝑖,𝑡 + 0.082 𝑅𝑆𝐼𝑍𝐸𝑖,𝑡− 2.40 𝐶𝐴𝑆𝐻𝑀𝑇𝐴𝑖,𝑡 + 0.054 𝑀𝐵𝑖,𝑡− 0.937 𝑃𝑅𝐼𝐶𝐸𝑖,𝑡 And:
NIMTAAVG is a profitability ratio, TLMTA is a debt ratio, EXRETAVG is an excess return measure, SIGMA is a volatility measure, RSIZE is a size measure, CAHMTA is a liquidity measure, MB is a market-to-book ratio and PRICE is a stock price measure.
The coefficients in the model is calculated by Campbell et al. (2008) and are based on U.S.
bankruptcy and failure data from 1963-2003. Because of the limited number of Norwegian listed firms and bankruptcies over the timespan of which we have available quarterly accounting data (2004-2018), we have found it best to use their best estimates instead of re- estimating the model ourselves on a limited dataset. The following paragraphs will include an explanation of each of the variables in the model, in addition to a discussion of the sign of the variables with regards to economic intuition. For the variables with a positive coefficient, an
8 Y=1 in the case of default and 0 otherwise
increase in the variable will lead to an increase in default probability, while the opposite applies for the variables with a negative coefficient.
We will start with NIMTA: Net Income to Market value of Total Assets9: 𝑁𝐼𝑀𝑇𝐴𝑖,𝑡 = 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒𝑖,𝑡
𝐹𝑖𝑟𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑒𝑞𝑢𝑖𝑡𝑦𝑖,𝑡 + 𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖,𝑡
NIMTA is a variable that represents the profitability of the firm for the past quarter, measured as net income divided by the market value of total assets. Campbell, Hilscher and Szilagyi found it better to use market value of total assets instead of the book value of total assets, as equity values are more sensitive to new information. High profitability is indicative of a firm in a good financial state, hence, an increase in NIMTA should lead to a decline in default probability, which is what we observe in our model. However, as the observant reader might have noticed, the model does not incorporate NIMTA directly, but rather the lagged variable NIMTAAVG.
𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑡−1,𝑡−12= 1 − 𝜃3
1 − 𝜃12 (𝑁𝐼𝑀𝑇𝐴𝑡−1,𝑡−3+ ⋯ + 𝜃9𝑁𝐼𝑀𝑇𝐴𝑡−10,𝑡−12)
That is, the historical weighted average of net income over market value of total assets is a preferred measure to NIMTA, which only incorporates the last quarter (Campbell et al. 2008).
𝜃 = 2−13 , which means that the weights are halved each quarter. That is, the most recent quarter has the weight 0.53, while the quarter that is farthest back in time has the weight 0.067.
In other words, the most recent quarter is allocated most weight. Obviously, the discussion regarding the sign of the variable still holds, hence an increase in NIMTAAVG leads to a decline in default probability, which is economically intuitive.
The next variable is TLMTA; Total book value of Liabilities over Market value of Total Assets:
𝑇𝐿𝑀𝑇𝐴𝑖,𝑡 = 𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖,𝑡
𝐹𝑖𝑟𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑒𝑞𝑢𝑖𝑡𝑦𝑖,𝑡 + 𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖,𝑡
9 Market value of total assets is in this thesis defined as market value of equity plus book value of liabilities.
How much leverage a firm holds is correlated with its default probability because financial leverage increases financial risk. A firm with high leverage will have more financial obligations to uphold and thereby the risk of default increases. Lagging TLMTA as done with NIMTA did not enter significantly in the regression analysis of Campbell, Hilscher and Szilagyi, and hence, TLMTA is calculated based on the last quarter. TLMTA enters the model with a positive sign, which implies that an increase in a company’s debt ratio will lead to an increase in default probability, which is economically intuitive.
EXRET is the natural logarithm of each firm’s excess stock return relative to the OSEBX:
𝐸𝑋𝑅𝐸𝑇𝑖,𝑡 = 𝐿𝑁(1 + 𝑅𝑖,𝑡) − 𝐿𝑁(1 + 𝑅𝑂𝑆𝐸𝐵𝑋,𝑡)
Excess return should be a good indicator of default risk as the measure evaluates the performance of a stock relative to the performance of the OSEBX, which is our benchmark for the Norwegian market. One can argue that the development of a stock price is determined by the available information in the market, and investors’ belief about the future prospects for the firm. When a stock performs better than the market for a given period, it implies that the investors believe in better prospects for the firm than for the market as a whole. On the other hand, a stock that underperforms relative to the market, is believed to have less favorable prospects than the market as a whole. EXRET enters the model with negative sign, indicating that a higher excess return will decrease the probability of default, which makes economic sense.
We would like to emphasize that we have used OSEBX as a benchmark instead of the S&P 500 index, which is used in the model of Campbell et al. (2008). Even though we use the coefficients that they have estimated, we use the model on Norwegian data, and thus, want to compare the returns relative to a benchmark reflecting the Norwegian market. The S&P 500 index reflects the U.S. market and incorporating this benchmark for Norwegian stocks will likely inflict a bias as the excess return can vary greatly depending on the development of the Norwegian market relative to the U.S. market.
As we can see from the model, EXRET enters the model as EXRETAVG, which is the monthly lagged EXRET over the past 12 months.
𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑡−1,𝑡−12 = 1 − 𝜃
1 − 𝜃12 (𝐸𝑋𝑅𝐸𝑇𝑡−1+ ⋯ + 𝜃11𝐸𝑋𝑅𝐸𝑇𝑡−12)
That is, a weighted average of excess returns is a preferred measure to EXRET which only incorporate the last month (Campbell et al., 2008). As earlier, 𝜃 = 2−13, which means that the weights are halved each month, putting most weight on the most recent development.
SIGMA represents the volatility of the stock returns:
𝑆𝐼𝐺𝑀𝐴𝑖,𝑡−1,𝑡−3 = (252 ∗ 1
𝑁 − 1∗ ∑ 𝑟𝑖,𝑘2
𝑘∈{𝑡−1,𝑡−2,𝑡−3}
)
1 2
SIGMA is a measure of the annualized standard deviation, calculated based on the previous three months daily stock returns (Campbell et al., 2008). It is a measure of the stock’s volatility. A stock is volatile in a period if the dispersion of the returns are high in that same period. Intuitively, high volatility, or high SIGMA, should then imply higher default risk, which is the case for our model since SIGMA enters the model with a positive sign.
The next variable is RSIZE, which is the natural logarithm of the firm’s market value divided by the combined market capitalization of all the firms in the market:
𝑅𝑆𝐼𝑍𝐸𝑖,𝑡 = 𝐿𝑁 ( 𝐹𝑖𝑟𝑚 𝑀𝑎𝑟𝑘𝑒𝑡 𝐸𝑞𝑢𝑖𝑡𝑦𝑖,𝑡 𝑇𝑜𝑡𝑎𝑙 𝑂𝑆𝐸 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒𝑖,𝑡)
RSIZE is a variable measuring the size of the companies relative to the size of the market.
Intuitively, one would expect that larger firms, measured in terms of market capitalization, would have less probability for default than smaller firms. However, several companies with large market capitalization have gone bankrupt over recent years, such as Kodak, Enron and Lehman Brothers, and there is not necessarily a positive relationship between being large and being able to uphold financial obligations. In this model, RSIZE enters with a positive coefficient, indicating that larger companies have a higher risk for default.
The model also includes a measure of liquidity through the variable CASHMTA:
𝐶𝐴𝑆𝐻𝑀𝑇𝐴𝑖,𝑡 = 𝐶𝑎𝑠ℎ 𝑎𝑛𝑑 𝑆ℎ𝑜𝑟𝑡 𝑇𝑒𝑟𝑚 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑚𝑒𝑛𝑡𝑠𝑖,𝑡
𝐹𝑖𝑟𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑒𝑞𝑢𝑖𝑡𝑦𝑖,𝑡+ 𝑇𝑜𝑡𝑎𝑙 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖,𝑡
Cash and short-term investments, which is the liquid assets of a company, is divided by the market value of total assets. Companies with a high level of liquid assets should have less
problems covering the interest payments on debt, and thus, the probability of bankruptcy should decrease with increasing CASHMTA ratio. As we can see from the model, CASHMTA enters the model with a negative sign, and thus, an increase in cash and short-term investments over market value of total assets decreases the default probability. Hence, the variable enters the model with the economically intuitive sign.
Market-to-book ratio is the second last variable in our model:
𝑀𝐵𝑖;𝑡 =𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦𝑖,𝑡 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦𝑖,𝑡
A high MB ratio indicates that the market interprets the company’s prospects as better than what is reflected in the book value of the firm. Hence, a high market-to-book ratio indicates that a company is expected to grow in the future. As MB enters the model with a positive coefficient, a higher market-to-book value indicates more risk and higher default probability.
Economically, this makes sense; a company whose equity is worth approximately the same as the net book value of assets should have less risk for a sudden drop in share price, as the share price does not reflect a high growth expectation in the future. However, companies that have a very low MB ratio are most likely firms with negative growth expectations, typically companies with outdated technology or companies that are in a mature segment. One can argue that these companies have a negative future prospect, and therefore should have higher risk for default than companies where the investors believe in high growth potential. On the other hand, our model is predicting default risk for the following month, and as Table II in Campbell et al. (2008, p. 2907) shows, bankrupt companies on average have a higher MB than the average of all companies. Thus, the MB variable seems to be entering the model with the economically intuitive sign. This is also in line with what Dichev (1998) presented in the article “Is the Risk of Bankruptcy a Systematic Risk?”. He found that distressed firms generally have low market-to-book ratio, but that the most distressed firms have high market- to-book ratio. This variable will be discussed in more detail in Chapter 6.
Finally, our last variable is PRICE, which is the natural logarithm of the price per share truncated above at 19.2 NOK:
𝑃𝑅𝐼𝐶𝐸𝑖𝑡 = 𝐿𝑁(𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒𝑖,𝑡)
The PRICE variable is the least intuitive variable in our model. Including this variable suggests that the price of the stock itself influences the probability of default. Campbell et al. (2008) expect that this variable is relevant for low share prices, arguing that NYSE and NASDAQ tend to delist stocks with a share price below $1 and that reverse stock splits done to prevent the $1 minimum level is a negative sign to the market. PRICE is meant to capture the fact that distressed companies tend to trade at lower share prices (Campbell et al., 2008). Following Campbell, Hilscher and Szilagyi, exploratory analysis suggests that price per share is relevant below $15 and thus, they truncate prize per share at this level before taking the natural logarithm. However, as we are dealing with Norwegian data, we find a suitable measure that is analogous to the $15 relevance area for the Norwegian stock exchanges. We found approximately 19 NOK to be representative for the $15 limit on the Norwegian stock exchanges. We will elaborate on this finding in Chapter 5. The PRICE variable enters the model with a negative sign, which is in line with the idea that distressed firms tend to trade at lower share prices.
In the last section of this chapter we will further elaborate on why we chose to replicate the model. We will also discuss the accuracy of the model on Norwegian data.
4.4 Model Evaluation
The first thing that is important to emphasise is the fact that this model was developed based on historical U.S. data. The most optimal would be to run our own regression on Norwegian data and use Norwegian bankruptcies and company failures as the dependent variable.
However, we have concluded that the number of bankruptcies among the listed companies in the period between 2004 and 2018, which is the years we have access to both quarterly data and stock price history, is insufficient in running a logit regression.
If we were to look at all Norwegian companies including those not listed, the dataset would contain enough bankruptcies to run a regression. However, then we would limit the access of data to accounting data from annual reports, which would influence the predictability of our model. In addition, such a model would be backward-looking, since the accounting data only represents what has happened in the past, without indicating anything about the future.
Furthermore, such a model would be estimated on all companies, but used only on listed companies, as we are dependent on stock price development to research the distress risk puzzle. Thus, such a model would rely on the assumption that the probability for default is
equal for companies that are listed and those that are not listed. Hence, we have found an approach where we use the coefficients estimated in the model developed by Campbell et al.
(2008) to be the best option.
The following paragraphs will evaluate the accuracy of the model on Norwegian data. In order to do this, we examine the model’s predictions of default probability for firms in our dataset, and match this with actual bankruptcy data from Norway. Data collection, data processing and the results from the analysis is discussed in later chapters.
The first measure we will conduct is to look at the average predicted default probability for the companies that went bankrupt in the period between 2004 and 2018. In the quarter before the companies went bankrupt, the average default probability was estimated at approximately 30%. This is well above the average default probabilities for the entire dataset. In fact, it is almost three times higher than the average default probability for the five percent most distressed stocks. Looking at the default probability for the companies in the quarter they went bankrupt, the estimated default probability is even higher and above 50%. This indicate that the model is suitable on Norwegian data.
To further validate the model on Norwegian data, we turn our attention to look at how many companies that have high estimated default probabilities, without actually going bankrupt. Of a total of 364 companies in our dataset, 10 companies have default probabilities above 30% in at least one quarter without going bankrupt, and six companies have above 50% default probability in at least one quarter without going bankrupt. Seven of the companies that had more than 30% default probability without officially going bankrupt, had news articles discussing the possibility that the companies would go bankrupt in the near future, and most of these firms conducted restructuring measures during the period in which they had a high default probability. Furthermore, only three companies that actually went bankrupt had less than 30% default probability before they went bankrupt. However, these companies had far higher default probabilities than the average company in the dataset. These findings further confirm that the model is suitable on Norwegian companies.
However, the findings also establish ground for discussing the differences between what is considered bankruptcy in the U.S. versus what is considered bankruptcy in Norway. In the U.S., companies can file for bankruptcy under Chapter 7 or Chapter 11. A Chapter 7 bankruptcy filing imply liquidation of the firm, and is equivalent to the Norwegian bankruptcy
procedure (United States Courts, 2018). The Chapter 11 bankruptcy filing, on the other hand, is known as the reorganization bankruptcy, where the distressed company usually proposes a plan for reorganization to the creditors in order to keep the business alive (United States Courts, 2018). In Norway, there is no equivalent to the Chapter 11 bankruptcy filing.
Companies can negotiate terms of the debt obligations and make restructuring plans with their creditors when in financial distress, but these companies will not get a bankruptcy status unless they fail to negotiate with the creditors. As mentioned in the previous paragraph, many of the companies with high default probability did restructuring measures when they were in high distress risk. It is likely that these companies would have been registered as bankrupt in the U.S. under Chapter 11. In Norway however, they will not be registered as bankrupt before the firms are liquidated. Thus, if the same rules did apply, the predictive power of the replicating model would have been even higher. This further validate the predictive power of Campbell et al. (2008) best model on Norwegian data.
After evaluating the accuracy of Campbell, Hilscher and Szilagyi’s model on Norwegian data, we feel comfortable in using their default probability measure as a proxy for distress risk on Norwegian data.
5. Data
Chapter 5 will focus on the process of collecting and handling the data that is necessary to estimate default probability for Norwegian firms. In addition, we will showcase and discuss the summary statistics for our final dataset.
5.1 Data Collection & Processing
The first part of this section will explain the dataset that we use for our default probability calculations, that is, which years we research and which stocks we include. Second, we will present the idea of lagging the accounting data to eliminate look-ahead bias10. After that, we will look closer into some of the more extensive variables in the model. Next, we will explain the idea behind winsorizing the variables to eliminate outliers, and shorty explain how we did this. In addition, we will elaborate on how we created portfolios based on default probability.
We use Compustat to collect quarterly accounting data on all Norwegian public companies that are, or have been, listed on Oslo Børs, Oslo Axess or Merkur Markets. As quarterly data were available only from 2004 and onwards, our dataset is limited to include data from the first quarter of 2004 to the second quarter of 2018. In order to gather market data, we used Datastream. Stock prices and market capitalization for all listed companies in Norway were collected from the beginning of 2000 until October 2018. That is, data on both active and inactive companies were collected. The collected data were merged and processed using excel, and a few companies were eliminated due to missing values in either accounting or market data. After the first elimination, 11 350 observations11 per variable, remained in our data set.
Consistent with Campbell et al. (2008) we lag the accounting data by two months. Lagging the accounting data is done to ensure that the last quarterly report is publicly available when the default probabilities are calculated. That is, lagging ensures that the model is tradeable; at any point in time, all information that is necessary for predicting default risk for the following
10 A look ahead bias occurs when estimating models that uses information that is not yet available.
11 Observation: A datapoint for one variable for one company in a specific quarter
month, is known to the market. Thus, lagging the accounting data by two months eliminates look-ahead bias.
In order to calculate the variable EXRETAVG, we start with calculating EXRET, which is the monthly excess return for a given company over the benchmark index. We selected OSEBX as our benchmark index and used the historical development of the index in order to calculate the monthly excess return. After that, we used EXRET to calculate EXRETAVG. In order to calculate this variable for a given company in a given quarter, 12-month stock price history must be available. This is only a challenge for companies that were listed shortly before or during the period of which we measure default risk (2004-2018). However, a significant number of firms are listed in the period, and so, eliminating all companies with less than 12- month stock history would be a severe loss given the limited number of years we have available data. Therefore, we chose to use a six-month average for the companies with less than 12 months of available data, and a three-month average for the companies with less than six months available data. The companies that had less than three-month stock history for a given quarter was eliminated from the data set. The companies themselves were not eliminated from the model, but excluded until they had more than three months of consecutive returns. In total, 139 observations per variable were eliminated in this action, leaving 11 211 observations.
Similar to EXRETAVG, the variable NIMTAAVG is created based on an underlying variable (NIMTA), and thus also depends on a consecutive history of observations. The NIMTA variable depend on both accounting data and market data, as net income is divided by the market value of total assets. That is, to create the NIMTAAVG variable, we need data on market capitalization, net income and liabilities for the past four quarters. Instead of eliminating all observations that do not fulfill the need for data, we take the average of the last three quarters for the companies that have less than four quarterly observations prior to the time of calculation, and the average of the last two quarters when there is less than three consecutive quarters of observations prior to the calculation date. For the companies that only have available data for the previous quarter, we use NIMTA.
SIGMA is calculated as the annualized standard deviation, computed based on the previous three months daily stock returns. Hence, we are dependent on stock prices for the previous three months in order to calculate this variable. As EXRETAVG is dependent on the same information, we do not need to eliminate any observations when constructing this variable,
nor do we have to collect any new information. For RSIZE, on the other hand, we need to collect some new information in order to calculate the relative size of the companies compared to the market. As no reliable sources were able to supply us with the historical total market capitalization of Oslo Børs, Oslo Axess and Merkur Markets, we constructed this measure ourselves by adding together the market capitalization of all the companies in our dataset each quarter. As our dataset is reasonably complete, this should be a good measure of the value of the total market. We also crosschecked this for some specific years using the Oslo Børs official webpage.
Consistent with Campbell et al. (2008), we adjust book value of equity (BVE) to eliminate outliers by adding 10% of the difference between market value of equity (MVE) and book value of equity to the book value of equity:
𝐵𝑉𝐸 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 1 = 𝐵𝑉𝐸 + 10% ∗ (𝑀𝑉𝐸 − 𝐵𝑉𝐸)
After this adjustment, the number of observations with negative book value of equity dropped from 174 observations to 102 observations. That is, less than 1% of the companies had a quarter with negative book value of equity. Campbell et al. (2008) chose to replace these negative values with a $1 positive value. We chose a different strategy; for the companies where the book value of equity was lower than 2.5% of the market value of equity after the first adjustment, we changed the book value of equity to 2.5% of the market value of equity.
This limits the MB variable to a maximum of 40, and is done to prevent the MB variable to be too decisive for the final default risk measure. Before doing this preventive measure, the MB variable reached very high levels for some of the observations, leading the default probability to be dependent solely on this single variable.
Another variable, that we have discussed previously, is PRICE. Campbell, Hilscher and Szilagyi truncate PRICE at $15 before taking the natural logarithm, arguing that the share price only is relevant for predicting distress risk under this $15 limit. In order to find a comparable measure for the $15 limit on the Norwegian exchanges, we measure the average percentile of which $15 represents on NYSE and NASDAQ based on stock prices in 2002-
200312. From this analysis we found that a stock price of $15 represents the 45-percentile on NYSE and NASDAQ, when all the stock prices are ranked in ascending order. The 45- percentile stock price on Oslo Børs, Oslo Axess and Merkur Markets for the same period is equivalent to approximately 19 NOK. Thus, we truncated price per share at 19 NOK, meaning that all shares with a share price higher than 19 NOK were adjusted down to 19 NOK, and that all shares with prices below 19 NOK kept their original price.
After creating all the variables needed to predict default probability, we eliminated all company observations were accounting data were missing. In total, 262 observations were missing, leaving the final dataset at 10 949 observations per variable. That is, our final dataset consists of 10 949 estimations of default probability, split between 364 different companies for the period between 2004 and 2018.
Following Campbell et al. (2008), we eliminate outliers for the variables using a method referred to as winsorizing. That is, we eliminate the tails of the distribution for all variables for each company, by changing the values below the 5th percentile to the 5th percentile and the values above the 95th percentile to the 95th percentile. This procedure was carried out accordingly for all the variables except for PRICE and MB. PRICE is not winsorized due to its intrinsic characteristics; it is already truncated above at 19 NOK and low share price is natural for distressed firms. The MB variable was adjusted such that the book value of equity was minimum 2.5% of the market value of equity. That is, we capped the maximum value of the variable to 40. Thus, we chose to only winsorize this variable from below, as we did not want to adjust the highest values. The procedure of winsorizing the variables was conducted using the programming tool R. The same tool was used for sorting the portfolios based on default probability, and for calculating the portfolio returns. The latter will be discussed in Chapter 6.
In this section we have explained the process of collecting and calculating the data necessary for using the model of Campbell et al. (2008) on Norwegian data. We have conducted some
12 We used the period from 2002 to 2003 to avoid look-ahead bias and to be in line with the exploratory analysis conducted in Campbell et al. 2008
minor adjustments on the variables in the model such that they better fit with our Norwegian dataset. The subsequent section summarizes the properties of our eight explanatory variables.
5.2 Summary Statistics
Table I summarizes the eight adjusted explanatory variables which are the input for our default probability model. Instead of looking at NIMTAAVG and EXRETAVG, we examine their building blocks, NIMTA and EXRET. This is in order to keep the format consistent with the other variables. We have separated the summary statistics table into two different panels. Panel A displays summary statistics for all observations in our dataset. As a result, the companies that have a long history as a listed company will have relatively more weight on the descriptive statistics than the companies that have a short history as a listed company. The advantage of measuring the summary statistics across all periods, like in Panel A, is that we capture the total distribution of the dataset. This is particularly important when studying the minimum and maximum values. Panel B, on the other hand, displays summary statistics across the companies in the dataset. We used the programming tool R to take the average of each variable for each company, and then calculate the descriptive statistics based on the companies averages. This method ensures that we avoid the bias of putting too much weight on the companies with many quarterly observations. However, it is important to remember that for the company specific descriptive statistics we don’t capture the full spread of observations, thus the minimum and maximum values are pulled closer to the mean. As a result, we have found it best to display both Panel A and Panel B, as both panels have some advantages.
Another aspect that is important to notice is that the variables are equal-weighted13 instead of value-weighted14. That is, firms with a small market capitalization have the same weight as firms with a large market capitalization. We will elaborate on the effect of equal-weighting relative to value-weighting in Chapter 6.3.
13 When calculating the average for an equal-weighted portfolio, each company’s observation is assigned the same weight.
14 When calculating the average for a value-weighted portfolio, each company´s observation is assigned a weight based on their size relative to the other companies. Normally measured as the market capitalization of the company divided by total market capitalization.
